This is essentially [1]}, but some effort is required to extract the statement as written above. As the proof is short we include it for clarity.
By [2]}, the cup-product filtration is uniquely defined by the two properties

\([Z] \cup -\)  maps \(K_i\)  into \(K_{i-2}\)  for all \(i \ge 2\) , and

the map
\([Z_{-r}] \cup -\colon \operatorname{Gr}^K_{n+r}H^*(Y,\mathbb {Q}) \longrightarrow \operatorname{Gr}^K_{n-r}H^*(Y,\mathbb {Q})\) 
is an isomorphism for all \(0 < r \le m = \dim _{\mathbb {C}}(B)\) .

To prove that \(K_{\bullet }\)  coincides with the shifted perverse Leray filtration, it suffices to show that the shifted perverse Leray filtration satisfies these two properties. Indeed, from the discussion above, we have
\([Z] \cup - : \operatorname{Gr}^P_{l + k - n}H^k(Y,\mathbb {Q}) \longrightarrow \operatorname{Gr}^P_{l+(k+2) - n - 2}H^{k+2}(Y,\mathbb {Q}),\) 
proving (1), and (2) is precisely Lemma REF .
